scholarly journals The extended F-expansion method and new exact solutions of the generalized KdV equation

2009 ◽  
Vol 58 (4) ◽  
pp. 2159
Author(s):  
Liang Li-Wei ◽  
Li Xing-Dong ◽  
Li Yu-Xia
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Expansion Method ◽  
Generalized Kdv Equation ◽  
New Exact Solutions

scholarly journals AKNS Formalism and Exact Solutions of KdV and Modified KdV Equations with Variable-Coefficients

2016 ◽  
Vol 6 ◽  
pp. 32-41 ◽  
Author(s):  
Supratim Das ◽  
Dibyendu Ghosh
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Elliptic Functions ◽  
Variable Coefficients ◽  
Jacobian Elliptic Functions ◽  
Generalized Kdv Equation ◽  
New Exact Solutions ◽  
Kdv Equations ◽  
Modified Kdv Equation ◽  
Modified Kdv Equations

We apply the AKNS hierarchy to derive the generalized KdV equation andthe generalized modified KdV equation with variable-coefficients. We system-atically derive new exact solutions for them. The solutions turn out to beexpressible in terms of doubly-periodic Jacobian elliptic functions.

New exact solutions for a generalized KdV equation

2018 ◽  
Vol 92 (2) ◽  
pp. 215-219 ◽  
Author(s):  
Lingfei Li ◽  
Yingying Xie ◽  
Shihui Zhu
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Generalized Kdv Equation ◽  
New Exact Solutions

scholarly journals F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ali Filiz ◽  
Mehmet Ekici ◽  
Abdullah Sonmezoglu
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
New Exact Solutions

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulusmof Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

New exact solutions to the generalized KdV equation with generalized evolution

Pramana ◽  
2012 ◽  
Vol 78 (4) ◽  
pp. 499-511 ◽  
Author(s):  
YONGAN XIE ◽  
SHENGQIANG TANG ◽  
DAHE FENG
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Generalized Kdv Equation ◽  
New Exact Solutions

SOLVING THE GENERALIZED BURGERS–KdV EQUATION BY A COMBINATION METHOD

2008 ◽  
Vol 22 (21) ◽  
pp. 2021-2025 ◽  
Author(s):  
YUANXI XIE
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Combination Method ◽  
Generalized Kdv Equation ◽  
Generalized Burgers Equation

In view of the analysis on the characteristics of the generalized Burgers equation, generalized KdV equation and generalized Burgers–KdV equation, a combination method is presented to seek the explicit and exact solutions to the generalized Burgers–KdV equation by combining with those of the generalized Burgers equation and generalized KdV equation. As a result, many explicit and exact solutions for the generalized Burgers–KdV equation are successfully obtained by this technique.

A Class of Exact Solutions of (3+1)-Dimensional Generalized B-Type Kadomtsev–Petviashvili Equation

2017 ◽  
Vol 18 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Shuang Liu ◽  
Yao Ding ◽  
Jian-Guo Liu
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Expansion Method ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
New Exact Solutions ◽  
Petviashvili Equation

AbstractBy employing the generalized$(G'/G)$-expansion method and symbolic computation, we obtain new exact solutions of the (3 + 1) dimensional generalized B-type Kadomtsev–Petviashvili equation, which include the traveling wave exact solutions and the non-traveling wave exact solutions showed by the hyperbolic function and the trigonometric function. Meanwhile, some interesting physics structure are discussed.

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